Brendan,
Is your friend's Cub equipped with a Command twin or a Courage twin? The Courage is even more sensitive to oil levels. As you know, the Courage block is different internally. The breather chamber was(up until late 2008) quite easily flooded with crankcase oil,this would be ingested from the breather hose and cause smoke on any inclines.
The same situation as with Command oil level is also an issue with the RH cylinder in my earlier explanation. The Courage must have the oil level checked while sitting on level ground,the dipstick is to be lowered onto the dipstick tube (not screwed on, contrary to earlier instructions). As mentioned, simply lower it to the fill tube and withdraw to check oil level.(Courage only, not Command!)Screwing the dipstick on will overfill the crankcase by approx 14 oz.; not good!
Remmember to insure that the tractor sits level, those slanting "downhill" will have a much greater propensity to smoke on startup!!
Now, if that is a Courage twin and nothing stops the excessive smoke on inclines, ask you dealer to call his regional service rep, either Cub or Kohler. Have the numbers from the engine data plate when he calls. Whether in warranty or not they typically will work with you to correct the issue as it was not an isolated problem. Be persistant; remember an engine that does that "may not" be emissions compliant, therefor leverage exists.